Generalized Ginzburg-Landau theory of pseudo-one-dimensional systems

A generalized Ginzburg-Landau theory is suggested to describe the phase transition of an array of weakly coupled pseudo-one-dimensional chains. Using a mean-field approximation, the coupled-chain problem is reduced to that of a single chain in an effective field. The finite-range correlations which develop along the chain are treated using exact one-dimensional solutions. The results obtained are then used to construct a generalized Ginzburg-Landau theory. We argue that this approach provides a means of treating the remaining slowly varying long-range fluctuations. Results are given for a variety of arrays consisting of Ising, classical Heisenberg, real and complex ${\psi }^4$ chains.